Gdp Deflator

GDP Deflator

Question one:

The GDP deflator is a price index that is derived from the real GDP and the nominal GDP, the GDP deflator is calculated by dividing the nominal GDP by the Real GDP and then multiplying by 100, in our case we use nominal expenditure and real expenditure because GDP is also measured using the expenditure method. Therefore we use the following formula to derive the price index:

Price index = (nominal GDP/ real GDP) X 100

The following table summarizes our results:

YEAR

RTDE

QTDE

INTL

1/127

GDP Deflator

1963

288.856

30.814

1.053

14.969

0.106675991

1964

307.559

34.037

1.058

2/127

GDP Deflator

16.106

0.110668197

1965

312.417

36.256

1.0643

17.616

0.116050023

1966

317.366

38.395

3/127

GDP Deflator

1.0691

18.757

0.120980193

1967

329.964

40.985

1.068

21.158

0.12421052

1968

341.032

4/127

GDP Deflator

44.39

1.0754

22.964

0.130163738

1969

341.179

46.853

1.0905

24.123

0.137326741

1970

5/127

GDP Deflator

349.045

51.27

1.0921

27.009

0.146886505

1971

357.267

57.323

1.0885

31.4

0.160448628

6/127

GDP Deflator

1972

372.979

64.466

1.089

38.674

0.17284083

1973

402.565

76.242

1.1071

47.119

0.189390533

7/127

GDP Deflator

1974

393.599

88.949

1.1477

52.197

0.225988887

1975

386.71

108.923

1.1439

58.383

8/127

GDP Deflator

0.281665848

1976

397.225

129.328

1.1443

64.97

0.325578702

1977

396.143

146.204

1.1273

9/127

GDP Deflator

74.595

0.369068745

1978

411.909

167.515

1.1247

85.77

0.406679631

1979

426.915

197.906

10 / 127

GDP Deflator

1.1299

98.131

0.463572374

1980

414.792

227.537

1.1378

114.923

0.548556867

1981

408.223

11 / 127

GDP Deflator

249.322

1.1474

138.363

0.610749517

1982

417.916

274.649

1.1288

154.909

0.65718709

1983

12 / 127

GDP Deflator

438.768

302.895

1.108

175.299

0.690330653

1984

450.949

326.498

1.1069

198.93

0.724024224

13 / 127

GDP Deflator

1985

464.316

354.291

1.1062

224.794

0.763038534

1986

487.33

388.179

1.0987

258.304

14 / 127

GDP Deflator

0.796542384

1987

513.083

428.721

1.0947

304.948

0.835578259

1988

553.461

488.953

1.0936

15 / 127

GDP Deflator

358.233

0.883446169

1989

569.719

537.279

1.0958

426.322

0.943059649

1990

566.238

16 / 127

GDP Deflator

1.1108

477.138

1991

548.532

581.897

1.0992

504.133

1.060825986

1992

549.543

17 / 127

GDP Deflator

605.295

1.0912

517.883

1.10145157

1993

561.346

638.4

1.0787

544.055

1.137266499

1994

18 / 127

GDP Deflator

580.092

675.164

1.0805

567.157

1.163891245

Question two:

Deriving the real money supply:

We derive the real money supply RM4 by dividing the nominal money supply by the price index:

YEAR

RTDE

QTDE

19 / 127

GDP Deflator

INTL

RM4

1963

288.856

30.814

1.053

14.969

0.106675991

140.3221089

20 / 127

GDP Deflator

1964

307.559

34.037

1.058

16.106

0.110668197

145.5341321

1965

312.417

36.256

1.0643

17.616

21 / 127

GDP Deflator

0.116050023

151.7966094

1966

317.366

38.395

1.0691

18.757

0.120980193

155.0419081

1967

329.964

22 / 127

GDP Deflator

40.985

1.068

21.158

0.12421052

170.3398393

1968

341.032

44.39

1.0754

22.964

0.130163738

23 / 127

GDP Deflator

176.4239434

1969

341.179

46.853

1.0905

24.123

0.137326741

175.6613454

1970

349.045

51.27

24 / 127

GDP Deflator

1.0921

27.009

0.146886505

183.8766609

1971

357.267

57.323

1.0885

31.4

0.160448628

195.7012683

25 / 127

GDP Deflator

1972

372.979

64.466

1.089

38.674

0.17284083

223.7550002

1973

402.565

76.242

1.1071

47.119

26 / 127

GDP Deflator

0.189390533

248.7927945

1974

393.599

88.949

1.1477

52.197

0.225988887

230.9715343

1975

386.71

27 / 127

GDP Deflator

108.923

1.1439

58.383

0.281665848

207.2775257

1976

397.225

129.328

1.1443

64.97

0.325578702

28 / 127

GDP Deflator

199.5523649

1977

396.143

146.204

1.1273

74.595

0.369068745

202.1168168

1978

411.909

167.515

29 / 127

GDP Deflator

1.1247

85.77

0.406679631

210.9031127

1979

426.915

197.906

1.1299

98.131

0.463572374

211.6843141

30 / 127

GDP Deflator

1980

414.792

227.537

1.1378

114.923

0.548556867

209.5006132

1981

408.223

249.322

1.1474

138.363

31 / 127

GDP Deflator

0.610749517

226.5462292

1982

417.916

274.649

1.1288

154.909

0.65718709

235.7152207

1983

438.768

32 / 127

GDP Deflator

302.895

1.108

175.299

0.690330653

253.9348343

1984

450.949

326.498

1.1069

198.93

0.724024224

33 / 127

GDP Deflator

274.7560003

1985

464.316

354.291

1.1062

224.794

0.763038534

294.6037323

1986

487.33

388.179

34 / 127

GDP Deflator

1.0987

258.304

0.796542384

324.2815513

1987

513.083

428.721

1.0947

304.948

0.835578259

364.9544452

35 / 127

GDP Deflator

1988

553.461

488.953

1.0936

358.233

0.883446169

405.4949953

1989

569.719

537.279

1.0958

426.322

36 / 127

GDP Deflator

0.943059649

452.0626034

1990

566.238

1.1108

477.138

1991

548.532

37 / 127

GDP Deflator

581.897

1.0992

504.133

1.060825986

475.2268576

1992

549.543

605.295

1.0912

517.883

1.10145157

38 / 127

GDP Deflator

470.1822706

1993

561.346

638.4

1.0787

544.055

1.137266499

478.3883115

1994

580.092

675.164

39 / 127

GDP Deflator

1.0805

567.157

1.163891245

487.2938108

Question 3:

Rate of inflation:

YEAR

RTDE

QTDE

INTL

40 / 127

GDP Deflator

RM4

1963

288.856

30.814

1.053

14.969

0.106675991

140.3221089

41 / 127

GDP Deflator

1964

307.559

34.037

1.058

16.106

0.110668197

145.5341321

0.037423662

1965

312.417

36.256

1.0643

42 / 127

GDP Deflator

17.616

0.116050023

151.7966094

0.048630284

1966

317.366

38.395

1.0691

18.757

0.120980193

155.0419081

43 / 127

GDP Deflator

0.042483148

1967

329.964

40.985

1.068

21.158

0.12421052

170.3398393

0.026701286

1968

341.032

44 / 127

GDP Deflator

44.39

1.0754

22.964

0.130163738

176.4239434

0.047928455

1969

341.179

46.853

1.0905

24.123

0.137326741

45 / 127

GDP Deflator

175.6613454

0.055030704

1970

349.045

51.27

1.0921

27.009

0.146886505

183.8766609

0.069613275

1971

46 / 127

GDP Deflator

357.267

57.323

1.0885

31.4

0.160448628

195.7012683

0.09233063

1972

372.979

64.466

1.089

47 / 127

GDP Deflator

38.674

0.17284083

223.7550002

0.077234703

1973

402.565

76.242

1.1071

47.119

0.189390533

248.7927945

0.09575112

48 / 127

GDP Deflator

1974

393.599

88.949

1.1477

52.197

0.225988887

230.9715343

0.193242784

1975

386.71

108.923

49 / 127

GDP Deflator

1.1439

58.383

0.281665848

207.2775257

0.246370347

1976

397.225

129.328

1.1443

64.97

0.325578702

50 / 127

GDP Deflator

199.5523649

0.155904079

1977

396.143

146.204

1.1273

74.595

0.369068745

202.1168168

0.133577666

1978

51 / 127

GDP Deflator

411.909

167.515

1.1247

85.77

0.406679631

210.9031127

0.101907533

1979

426.915

197.906

1.1299

98.131

52 / 127

GDP Deflator

0.463572374

211.6843141

0.139895728

1980

414.792

227.537

1.1378

114.923

0.548556867

209.5006132

0.183325189

53 / 127

GDP Deflator

1981

408.223

249.322

1.1474

138.363

0.610749517

226.5462292

0.113375027

1982

417.916

274.649

54 / 127

GDP Deflator

1.1288

154.909

0.65718709

235.7152207

0.076033746

1983

438.768

302.895

1.108

175.299

0.690330653

253.9348343

55 / 127

GDP Deflator

0.050432462

1984

450.949

326.498

1.1069

198.93

0.724024224

274.7560003

0.048807874

1985

464.316

56 / 127

GDP Deflator

354.291

1.1062

224.794

0.763038534

294.6037323

0.053885365

1986

487.33

388.179

1.0987

258.304

57 / 127

GDP Deflator

0.796542384

324.2815513

0.043908464

1987

513.083

428.721

1.0947

304.948

0.835578259

364.9544452

0.049006652

58 / 127

GDP Deflator

1988

553.461

488.953

1.0936

358.233

0.883446169

405.4949953

0.057287165

1989

569.719

537.279

1.0958

59 / 127

GDP Deflator

426.322

0.943059649

452.0626034

0.067478339

1990

566.238

1.1108

477.138

60 / 127

GDP Deflator

0.060378314

1991

548.532

581.897

1.0992

504.133

1.060825986

475.2268576

0.060825986

1992

549.543

61 / 127

GDP Deflator

605.295

1.0912

517.883

1.10145157

470.1822706

0.03829618

1993

561.346

638.4

1.0787

544.055

1.137266499

62 / 127

GDP Deflator

478.3883115

0.032516118

1994

580.092

675.164

1.0805

567.157

1.163891245

487.2938108

0.023411176

The above table summarizes the rate of inflation, we cannot derive the rate of inflation for the year 1963 due to the fact that we need the price index for the year 1962 which is not provided

63 / 127

GDP Deflator

by our data.

Question 4:

Real interest rates:

RINTL = INTL – PI

YEAR

RTDE

QTDE

INTL

RM4

64 / 127

GDP Deflator

RINTL

1963

288.856

30.814

1.053

14.969

0.106675991

140.3221089

65 / 127

GDP Deflator

1964

307.559

34.037

1.058

16.106

0.110668197

145.5341321

0.037423662

1.0205763

1965

312.417

36.256

66 / 127

GDP Deflator

1.0643

17.616

0.116050023

151.7966094

0.048630284

1.0156697

1966

317.366

38.395

1.0691

18.757

67 / 127

GDP Deflator

0.120980193

155.0419081

0.042483148

1.0266169

1967

329.964

40.985

1.068

21.158

0.12421052

170.3398393

0.026701286

68 / 127

GDP Deflator

1.0412987

1968

341.032

44.39

1.0754

22.964

0.130163738

176.4239434

0.047928455

1.0274715

1969

69 / 127

GDP Deflator

341.179

46.853

1.0905

24.123

0.137326741

175.6613454

0.055030704

1.0354693

1970

349.045

51.27

70 / 127

GDP Deflator

1.0921

27.009

0.146886505

183.8766609

0.069613275

1.0224867

1971

357.267

57.323

1.0885

31.4

0.160448628

71 / 127

GDP Deflator

195.7012683

0.09233063

0.9961694

1972

372.979

64.466

1.089

38.674

0.17284083

223.7550002

0.077234703

72 / 127

GDP Deflator

1.0117653

1973

402.565

76.242

1.1071

47.119

0.189390533

248.7927945

0.09575112

1.0113489

1974

73 / 127

GDP Deflator

393.599

88.949

1.1477

52.197

0.225988887

230.9715343

0.193242784

0.9544572

1975

386.71

108.923

1.1439

74 / 127

GDP Deflator

58.383

0.281665848

207.2775257

0.246370347

0.8975297

1976

397.225

129.328

1.1443

64.97

0.325578702

75 / 127

GDP Deflator

199.5523649

0.155904079

0.9883959

1977

396.143

146.204

1.1273

74.595

0.369068745

202.1168168

0.133577666

0.9937223

76 / 127

GDP Deflator

1978

411.909

167.515

1.1247

85.77

0.406679631

210.9031127

0.101907533

1.0227925

1979

426.915

77 / 127

GDP Deflator

197.906

1.1299

98.131

0.463572374

211.6843141

0.139895728

0.9900043

1980

414.792

227.537

1.1378

78 / 127

GDP Deflator

114.923

0.548556867

209.5006132

0.183325189

0.9544748

1981

408.223

249.322

1.1474

138.363

0.610749517

226.5462292

79 / 127

GDP Deflator

0.113375027

1.034025

1982

417.916

274.649

1.1288

154.909

0.65718709

235.7152207

0.076033746

1.0527663

80 / 127

GDP Deflator

1983

438.768

302.895

1.108

175.299

0.690330653

253.9348343

0.050432462

1.0575675

1984

450.949

81 / 127

GDP Deflator

326.498

1.1069

198.93

0.724024224

274.7560003

0.048807874

1.0580921

1985

464.316

354.291

1.1062

224.794

82 / 127

GDP Deflator

0.763038534

294.6037323

0.053885365

1.0523146

1986

487.33

388.179

1.0987

258.304

0.796542384

324.2815513

83 / 127

GDP Deflator

0.043908464

1.0547915

1987

513.083

428.721

1.0947

304.948

0.835578259

364.9544452

0.049006652

1.0456933

84 / 127

GDP Deflator

1988

553.461

488.953

1.0936

358.233

0.883446169

405.4949953

0.057287165

1.0363128

1989

569.719

537.279

85 / 127

GDP Deflator

1.0958

426.322

0.943059649

452.0626034

0.067478339

1.0283217

1990

566.238

1.1108

477.138

86 / 127

GDP Deflator

477.138

0.060378314

1.0504217

1991

548.532

581.897

1.0992

504.133

1.060825986

475.2268576

0.060825986

87 / 127

GDP Deflator

1.038374

1992

549.543

605.295

1.0912

517.883

1.10145157

470.1822706

0.03829618

1.0529038

1993

88 / 127

GDP Deflator

561.346

638.4

1.0787

544.055

1.137266499

478.3883115

0.032516118

1.0461839

1994

580.092

675.164

89 / 127

GDP Deflator

1.0805

567.157

1.163891245

487.2938108

0.023411176

1.0570888

Question 5:

Estimate RM4t=

The following table summarizes the calculations:

90 / 127

GDP Deflator

Y-Y’

X-X’

YEAR

RM4

RINTL

91 / 127

GDP Deflator

1964

145.5341

1.020576

-129.289

-0.0012

0.155314

1.4431E-06

16715.58

1965

92 / 127

GDP Deflator

151.7966

1.01567

-123.026

-0.00611

0.751434

3.7307E-05

15135.46

1966

155.0419

1.026617

-119.781

93 / 127

GDP Deflator

0.004839

-0.57965

2.3418E-05

14347.48

1967

170.3398

1.041299

-104.483

0.019521

-2.03962

0.00038107

10916.7

94 / 127

GDP Deflator

1968

176.4239

1.027472

-98.3989

0.005694

-0.56027

3.2421E-05

9682.347

1969

175.6613

1.035469

95 / 127

GDP Deflator

-99.1615

0.013692

-1.35769

0.00018746

9833.006

1970

183.8767

1.022487

-90.9462

0.000709

-0.06449

96 / 127

GDP Deflator

5.0282E-07

8271.211

1971

195.7013

0.996169

-79.1216

-0.02561

2.026166

0.00065578

6260.226

1972

97 / 127

GDP Deflator

223.755

1.011765

-51.0679

-0.01001

0.511308

0.00010025

2607.926

1973

248.7928

1.011349

-26.0301

-0.01043

98 / 127

GDP Deflator

0.271461

0.00010876

677.5643

1974

230.9715

0.954457

-43.8513

-0.06732

2.952089

0.00453204

1922.939

99 / 127

GDP Deflator

1975

207.2775

0.89753

-67.5453

-0.12425

8.392371

0.01543756

4562.372

1976

199.5524

0.988396

100 / 127

GDP Deflator

-75.2705

-0.03338

2.512658

0.00111434

5665.647

1977

202.1168

0.993722

-72.706

-0.02806

2.03979

0.0007871

101 / 127

GDP Deflator

5286.169

1978

210.9031

1.022792

-63.9197

0.001015

-0.06487

1.0299E-06

4085.734

1979

211.6843

102 / 127

GDP Deflator

0.990004

-63.1385

-0.03177

2.006124

0.00100955

3986.476

1980

209.5006

0.954475

-65.3222

-0.0673

103 / 127

GDP Deflator

4.396371

0.00452967

4266.996

1981

226.5462

1.034025

-48.2766

0.012247

-0.59126

0.00015

2330.633

104 / 127

GDP Deflator

1982

235.7152

1.052766

-39.1076

0.030989

-1.21189

0.00096029

1529.407

1983

253.9348

1.057568

-20.888

105 / 127

GDP Deflator

0.03579

-0.74758

0.00128092

436.3096

1984

274.756

1.058092

-0.06686

0.036314

-0.00243

0.00131874

106 / 127

GDP Deflator

0.00447

1985

294.6037

1.052315

19.78087

0.030537

0.604049

0.00093251

391.2829

1986

324.2816

107 / 127

GDP Deflator

1.054792

49.45869

0.033014

1.632825

0.00108992

2446.162

1987

364.9544

1.045693

90.13159

0.023916

2.155562

108 / 127

GDP Deflator

0.00057196

8123.703

1988

405.495

1.036313

130.6721

0.014535

1.899346

0.00021127

17075.21

1989

109 / 127

GDP Deflator

452.0626

1.028322

177.2397

0.006544

1.159862

4.2824E-05

31413.93

1990

477.138

1.050422

202.3151

110 / 127

GDP Deflator

0.028644

5.795126

0.00082048

40931.42

1991

475.2269

1.038374

200.404

0.016596

3.325982

0.00027544

40161.76

111 / 127

GDP Deflator

1992

470.1823

1.052904

195.3594

0.031126

6.080794

0.00096884

38165.3

1993

478.3883

1.046184

112 / 127

GDP Deflator

203.5655

0.024406

4.96827

0.00059567

41438.89

1994

487.2938

1.057089

212.471

0.035311

7.502603

113 / 127

GDP Deflator

0.00124688

45143.91

total

8519.509

31.67511

6.66E-16

53.91976

0.03940544

393811.7

mean

114 / 127

GDP Deflator

274.8229

1.021778

B = ∑yx/∑x

B = 53.91976/0.03940544

B = 1368.332775

A = -1123.308961

We state the model as follows:

115 / 127

GDP Deflator

RM4t= – 1123.308961 + 1368.332775 RINTL

Question 6:

RM4t= – 1123.308961 + 1368.332775 RINTL

The following model has a constant and a slope value, from the model it is evident that if we hold all other factors constant and let the value of RINTL to be zero then the value of RM4 will be – 1123.308961, also if we hold all other factors constant and increase RINTL by one unit then RM$ will increase by 1368 units. From our result there it means that an increase in the real interest rate will increase the level of real money supply.

Coefficients:

We test the significance of the autonomous value and slope value at 98% level of test:

We state the null and alternative hypothesis in both cases, we start with the autonomous value :

Null hypothesis H0: a = 0, alternative hypothesis Ha: a ≠ 0. For the slope we state the null hypothesis as H0: b = 0 and the alternative hypothesis as Ha: b ≠ 0. We test both of this hypothesis at 95% level of test taking into consideration the sample size and also a two tail test, the critical value is 2.04523. after determining the standard errors of our coeeficients the following is the results:

coefficient

116 / 127

GDP Deflator

value

std error

T calculated T critical 95% null hypothesis

-1123.30896

529.199369

-2.1226574

2.04523

reject

117 / 127

GDP Deflator

1368.332775

3012.45646

0.45422491

2.04523

The table summarizes the T calculated values, from the above it is evident that we reject the null hypothesis for the autonomous value because the T calculated is greater than the T critical, we accept the null hypothesis for the slope because the T calculated is smaller than the T critical.

For this reason therefore at 95% level of test the autonomous value is statistically significant while at the same level of test the slope value is not statistically significant.

Question 7:

We now estimate the model

118 / 127

GDP Deflator

RM4t= a + b1RINTL + b2RDTE

After estimating the model is stated as follows:

RM4t= – 534.66+ 267.9 RINTL + 1.24 RDTE

This model means that if we hold all factors constant and that the value of b1 and b2 are zero then the value of RM4 will be -534.66, if we hold all factors constant and increase the value of RINTL by one unit then RM4 will increase by 267.9 units, finally if we hold all other factors constant and increase RDTE by one unit then the level of RM4 will increase by 1.24 units.

Statistical significance of the data shows the following results:

Null hypothesis H0: a = 0, alternative hypothesis Ha: a ≠ 0. For b1 we state the null hypothesis

as H0: b1 = 0 and the alternative hypothesis as Ha: b1 ≠ 0, For b2 we state the null hypothesis as H0: b2 = 0 and the alternative hypothesis as Ha: b2 ≠ 0. We test this hypothesis at 95% level of test taking into consideration the sample size and also a two tail test, the critical value is 2.04841. After determining the standard errors of our coefficients the following is the results:

coefficient

value

standard deviation

T calculated

119 / 127

GDP Deflator

T critical 95% null hypothesis

(534.66)

109.1178754

(4.90)

2.04841

reject

267.9060968

106.7331702

120 / 127

GDP Deflator

2.51

2.04841

reject

1.24

1.286465098

0.97

2.04841

The table summarizes the T calculated values, from the above it is evident that we reject the null hypothesis for the a because the T calculated is greater than the T critical, we also reject the null hypothesis for the b1 because the T calculated is greater than the T critical, we however accept the null hypothesis b2 because the T calculated is smaller than the T critical.

121 / 127

GDP Deflator

For this reason therefore at 95% level of test both the autonomous value and b1 are statistically significant while b2is not statistically significant at 95% level of test.

Question 8:

We now estimate the model

RM4t= a + b1RINTL + b2PI

After estimating the model is stated as follows:

RM4t= -701826551.6 + 686607260.3RINTL + 3279238.325 PI

This model means that if we hold all factors constant and that the value of b1 and b2 are zero then the value of RM4 will be -701826551.6, if we hold all factors constant and increase the value of RINTL by one unit then RM4 will increase by 686607260.3 units, finally if we hold all other factors constant and increase PI by one unit then the level of RM4 will increase by 3279238.325 units.

Statistical significance of the data shows the following results:

Null hypothesis H0: a = 0, alternative hypothesis Ha: a ≠ 0. For b1 we state the null hypothesis

122 / 127

GDP Deflator

coefficient

value

standard deviation

T calcualted T critical 95% null hypothesis

-701826551.6

132613646.1

-5.292265

2.04841

reject

123 / 127

GDP Deflator

686607260.3

129773744.2

5.2908026

2.04841

reject

3279238.325

2496305049

0.0013136

2.04841

124 / 127

GDP Deflator

For this reason therefore at 95% level of test both the autonomous value and b1 are statistically significant while b2is not statistically significant at 95% level of test. The coefficient of PI in this model means that as inflation increase then the real money supply will also increase.

Question 10:

Joint hypothersis testing:

Null hypothesis:

H0: b1 = b2 = 0

Alternative hypothesis:

Ha: b1 ≠ b2 ≠0

125 / 127

GDP Deflator

Given that the value of F is derived from the following formula:

f = ((b1yx1 +b2yx2)/2 ) / (e2/n-3)

we use the following figures:

686607260.3

3279238.325

yx1

8726.598196

yx2

286875.8435

126 / 127

GDP Deflator

1.5265E+19

After calulcation our F value is 0.0000063580, from the table we use the F table to determine the critical value, for our case the critical value is using the 2 degrees of freedom for the numerator and 28 degrees of freedom for the denominator 5.453, this means that we accept the null hypothesis because the critical value is greater than our calculated value, therefore this means that b1 and b2 are not statistically significant.

References:

ONS database

127 / 127

Minutes To Drive To Work

Statistics 1

Statistics

Anova And Nonparametric Methods

Critical Writing 2

Sampling

Plagiarism

Regression Analyses Using Excel

References:

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